FIR Filter Coefficient Quantization Calculator

Estimate fixed-point coefficient word-length needed for an FIR filter to meet a given stopband attenuation after quantization.

Calculator Electronics Updated Apr 23, 2026
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How to Use
  1. Enter required stopband attenuation (dB) and filter length N.
  2. Tool estimates minimum coefficient word-length (bits) to preserve the stopband spec.
Input
dB
taps
Presets
Quantization Tradeoff
Min Bits
—
Rec. Bits
—
Q format
—
Taps · Bits
—bits

Show Work

Enter values.

Formulas

Quant noise floor
~6·B − 4 − 10·log(N) dB
Below ideal response.
Solve for B
B = (A_s + 4 + 10·log N) / 6
Round up.
+6 dB/bit
Each extra bit
Doubles precision.
Typical Q
Q1.15 (16 bit)
Fractional with sign.
High-perf
Q1.23 (24 bit)
Audio-grade.
HW alignment
8, 16, 18, 24, 32 bit
Match DSP/FPGA word.

History of Fixed-Point Filter Design

Alan Oppenheim and Ron Schafer's 1975 textbook Digital Signal Processing formalized coefficient-quantization analysis - showing that filter stopband attenuation is limited by ~(6B - 4) dB where B is the coefficient word length. Texas Instruments' TMS32010 (1982, first commercial DSP chip) had 16-bit coefficient storage, limiting filters to ~90 dB stopband. Modern audio DSPs and FPGAs use 18-32 bit coefficients for professional audio applications.

About This Calculator

Enter required stopband attenuation (dB) and FIR filter length (number of taps). The tool estimates minimum coefficient word-length B = (A_s + 4 + 10·log(N))/6 and recommends nearest hardware-friendly word size (16, 18, 24 bits).

For real designs, use Matlab\'s fxpconvert, Python\'s scipy.signal.firwin2 + quantization, or your FPGA vendor\'s filter-synthesis tool. This is a first-pass estimate for specification purposes. Everything runs client-side.

Frequently Asked Questions

Why quantize?

Fixed-point DSPs and FPGAs use finite-precision coefficient storage. Rounding off bits distorts the ideal frequency response — especially stopband. More bits = better fidelity but more hardware.

Rule of thumb?

Word length B bits gives ~(6B − 4) dB stopband attenuation limit. For 80 dB: need ≥ 14-bit coefs. For 100 dB: ≥ 18-bit. Adds ~6 dB per extra bit.

Floating point?

Single-precision IEEE 754 gives ~24 mantissa bits → ~140 dB — more than any practical filter needs. Double precision is overkill for DSP. Fixed-point (Q format) wins on power and throughput.

Common Use Cases

Audio ADC Decimator

96 dB target: use 18-20 bit coefficients on Q1.17 format.

Software Radio

80 dB adjacent-channel rejection: 16-bit coefs are minimum.

FPGA Implementation

Xilinx DSP48 multiplier: 18×18 bit → 80+ dB filter achievable.

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